The invention relates to a self-propelled construction machine, comprising a machine frame supported by a chassis having wheels or crawler tracks. The basic principle of the invention involves determining a variable Δ which is characteristic of the milling profile on the basis of a functional relationship between the variable which is characteristic of the milling profile and the advance speed v and/or milling drum rotational speed n. The variable Δ which is characteristic of the milling profile is a correction variable for adjusting the height of the milling drum with respect to the surface of the ground.